arXiv subjects

Amir Haji-Akbari

Publications and source records attributed to Amir Haji-Akbari.

29 records · Page 2Linked to original sources

arXiv2015

Strong Orientational Coordinates and Orientational Order Parameters For Symmetric Objects

Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in self-assembly and in inducing complex order. The problem of identifying different types of order that can emerge in such systems can, however, be challenging. Here, we revisit the problem of quantifying orientational order in systems of building blocks with non-trivial rotational symmetries. We first propose a systematic way of constructing orientational coordinates for such symmetric building blocks. We call the arising tensorial coordinates strong orientational coordinates (SOCs) as they fully and exclusively specify the orientation of a symmetric object. We then use SOCs to describe and quantify local and global orientational order, and spatiotemporal orientational correlations in systems of symmetric building blocks. The SOCs and the orientational order parameters developed in this work are not only useful in performing and analyzing computer simulations of symmetric molecules or particles, but can also be utilized for the efficient storage of rotational information in long trajectories of evolving many-body systems.

cond-mat.mtrl-sci↗

arXiv2015

Computational investigation of structure, dynamics and nucleation kinetics of a family of modified Stillinger-Weber model fluids in bulk and free-standing thin films

In recent decades, computer simulations have found increasingly widespread use as powerful tools of studying phase transitions in wide variety of systems. In the particular and very important case of aqueous systems, the commonly used force-fields tend to offer quite different predictions with respect to a wide range of thermodynamic and kinetic properties, including the ease of ice nucleation, the propensity to freeze at a vapor-liquid interface, and the existence of a liquid-liquid phase transition. It is thus of fundamental and practical interest to understand how different features of a given water model affect its thermodynamic and kinetic properties. In this work, we use the forward-flux sampling technique to study the crystallization kinetics of a family of modified Stillinger-Weber (SW) potentials with energy ($ε$) and length ($σ$) scales taken from the monoatomic water (mW) model, but with different tetrahedrality parameters ($λ$). By increasing $λ$ from 21 to 24, we observe the nucleation rate increases by 48 orders of magnitude at a supercooling of $ζ=T/T_m=0.845$. Using classical nucleation theory, we are able to demonstrate that this change can largely be accounted for by the increase in $|Δμ|$, the thermodynamic driving force. We also perform rate calculations in freestanding thin films of the supercooled liquid, and observe a crossover from a surface-enhanced crystallization at $λ= 21$ to a bulk-dominated crystallization for $λ\ge22$.

cond-mat.stat-mech↗

arXiv2015

Dimer Covering and Percolation Frustration

Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by non-overlapping dimers has not evidently been considered. Here, we propose a novel procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the square and the triangular lattice, on the remaining bonds connecting the dimers. We obtain $p_c=0.367713(2)$ and $p_c=0.235340(1)$ for random coverings of the square and the triangular lattice, respectively. We observe that the percolation frustration induced as a result of dimer covering is larger in the low-coordination-number square lattice. There is also no relationship between the existence of long-range order in a covering of the square lattice, and its percolation threshold. In particular, an ordered covering of the square lattice, denoted by shifted covering in this work, has an unusually low percolation threshold, and is topologically identical to the triangular lattice. This is in contrast to the other ordered dimer coverings considered in this work, which have higher percolation thresholds than the random covering. In the case of the triangular lattice, the percolation thresholds of the ordered and random coverings are very close, suggesting the lack of sensitivity of the percolation threshold to microscopic details of the covering in highly-coordinated networks.

cond-mat.stat-mech↗

arXiv2015

Direct Calculation of Ice Homogeneous Nucleation Rate for a Molecular Model of Water

Ice formation is ubiquitous in nature, with important consequences in a variety of environments, including biological cells, soil, aircraft, transportation infrastructure and atmospheric clouds. However, its intrinsic kinetics and microscopic mechanism are difficult to discern with current experiments. Molecular simulations of ice nucleation are also challenging, and direct rate calculations have only been performed for coarse-grained models of wate. For molecular models, only indirect estimates have been obtained, e.g. by assuming the validity of classical nucleation theory. We use a path sampling approach to perform the first direct rate calculation of homogeneous nucleation of ice in a molecular model of water. We use TIP4P/Ice, the most accurate among existing molecular models for studying ice polymorphs. By using a novel topological approach to distinguish different polymorphs, we are able to identify a freezing mechanism that involves a competition between cubic and hexagonal ice in the early stages of nucleation. In this competition, the cubic polymorph takes over since the addition of new topological structural motifs consistent with cubic ice leads to the formation of more compact crystallites. This is not true for topological hexagonal motifs, which give rise to elongated crystallites that are not able to grow. This leads to transition states that are rich in cubic ice, and not the thermodynamically stable hexagonal polymorph. This mechanism provides a molecular explanation to the earlier experimental and computational observations of the preference for cubic ice in the literature.

physics.chem-ph↗

arXiv2014

Suppression of Sub-surface Freezing in Free-Standing Thin Films of a Coarse-grained Model of Water

Freezing in the vicinity of water-vapor interfaces is of considerable interest to a wide range of disciplines, most notably the atmospheric sciences. In this work, we use molecular dynamics and two advanced sampling techniques, forward flux sampling and umbrella sampling, to study homogeneous nucleation of ice in free-standing thin films of supercooled water. We use a coarse-grained monoatomic model of water, known as mW, and we find that in this model a vapor-liquid interface suppresses crystallization in its vicinity. This suppression occurs in the vicinity of flat interfaces where no net Laplace pressure in induced. Our free energy calculations reveal that the pre-critical crystalline nuclei that emerge near the interface are thermodynamically less stable than those that emerge in the bulk. We investigate the origin of this instability by computing the average asphericity of nuclei that form in different regions of the film, and observe that average asphericity increases closer to the interface, which is consistent with an increase in the free energy due to increased surface-to-volume ratios.

cond-mat.stat-mech↗

arXiv2014

The Effect of Substrate on Thermodynamic and Kinetic Anisotropies in Atomic Thin Films

Glasses have a wide range of technological applications. The recent discovery of ultrastable glasses that are obtained by depositing the vapor of a glass-forming liquid onto the surface of a cold substrate has sparked renewed interest in the effects of confinements on physicochemical properties of liquids and glasses. Here we use molecular dynamics simulations to study the effect of substrate on thin films of a model glass-forming liquid, the Kob-Andersen binary Lennard-Jones system, and compute profiles of several thermodynamic and kinetic properties across the film. We observe that the substrate can induce large oscillations in profiles of thermodynamic properties such as density, composition and stress, and we establish a correlation between the oscillations in total density and the oscillations in normal stress. We also demonstrate that the kinetic properties of an atomic film can be readily tuned by changing the strength of interactions between the substrate and the liquid. Most notably, we show that a weakly attractive substrate can induce the emergence of a highly mobile region in its vicinity. In this highly mobile region, structural relaxation is several times faster than in the bulk, and the exploration of the potential energy landscape is also more efficient. In the subsurface region near a strongly attractive substrate, however, the dynamics is decelerated and the sampling of the potential energy landscape becomes less efficient than the bulk. We explain these two distinct behaviors by establishing a correlation between the oscillations in kinetic properties and the oscillations in lateral stress. Our findings offer interesting opportunities for designing better substrates for the vapor deposition process or developing alternative procedures for situations where vapor deposition is not feasible.

cond-mat.stat-mech↗

arXiv2013

Packing and Self-assembly of Truncated Triangular Bipyramids

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction $ϕ_{\max}$ changes continuously with the truncation parameter $t$. Eight distinct packings are identified based on discontinuities in the first and second derivatives of $ϕ_{\max}(t)$. These packings differ in the number of particles in the fundamental domain (unit cell) and the type of contacts between the particles. In particular, we report two packings with four particles in the unit cell for which both $ϕ_{\max}(t)$ and $ϕ'_{\max}(t)$ are continuous and the discontinuity occurs in the second derivative only. In the self-assembly simulations that we perform for larger boxes with 2048 particles, only one out of eight packings is found to assemble. In addition, the degenerate quasicrystal reported previously for triangular bipyramids without truncation [{http://prl.aps.org/abstract/PRL/v107/i21/e215702}{Haji-Akbari \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{107}: 215702 (2011)}] assembles for truncations as high as 0.45. The self-assembly propensities for the structures formed in the thermodynamic limit are explained using the isoperimetric quotient of the particles and the coordination number in the disordered fluid and in the assembled structure.

cond-mat.stat-mech↗

arXiv2011

Phase Diagram of Hard Tetrahedra

Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal of triangular bipyramids (dimers) with packing density 4000/4671=85.63%. In simulation a dodecagonal quasicrystal is observed; its approximant, with periodic tiling (3.4.3^2.4), can be compressed to a packing fraction of 85.03%. Here, we show that the quasicrystal approximant is more stable than the dimer crystal for packing densities below 84% using Monte Carlo computer simulations and free energy calculations. To carry out the free energy calculations, we use a variation of the Frenkel-Ladd method for anisotropic shapes and thermodynamic integration. The enhanced stability of the approximant can be attributed to a network substructure, which maximizes the free volume (and hence the 'wiggle room') available to the particles and facilitates correlated motion of particles, which further contributes to entropy and leads to diffusion for packing densities below 65%. The existence of a solid-solid transition between structurally distinct phases not related by symmetry breaking -- the approximant and the dimer crystal-- is unusual for hard particle systems.

cond-mat.soft↗

arXiv2011

Degenerate Quasicrystal of Hard Triangular Bipyramids

We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.

cond-mat.stat-mech↗

arXiv2010

Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of ϕ = π/\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with ϕ = 0.7786, which was subsequently compressed numerically to ϕ = 0.7820. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of ϕ = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is ϕ = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams, and compresses to ϕ = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

cond-mat.soft↗

arXiv2009

Percolation in Networks with Voids and Bottlenecks

A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled checkerboard and "stack-of-triangle" lattices. Thresholds for the checkerboard lattices of different mesh sizes are estimated using the gradient percolation method, while for the triangular system they are found exactly using the triangle-triangle transformation. The values of the thresholds approach the asymptotic values of 0.64222 and 0.53993 respectively as the mesh is made finer, consistent with a direct determination based upon the predicted critical corner-connection probability.

cond-mat.stat-mech↗